-4-
and it.2 V/qi would represent an approximate 95 percent confidence
interval for the successive coefficient it+l"
Clearly estimation of the varying parameters must be referenced to
some point during the sample period. Because interest is focused on
forecasting, we desire the value of the parameters given the most recent
observation. The values taken by the parameters given all observations
through the most recent will be denoted T*. To estimate BT, Sant (1977)
has formulated a generalized least squares model of the form
YT = X TT + ET ATUT (4)
where
X1 1X X1 X1 112
AT = 0 x2. x2 x2 and UT= 3
0 0 .0 xT-1 "lT-1
0 0 0 0 0
Alternatively (4) may be written compactly
YT = XT8T + VT (5)
Here YT and XT represent the customary TXl regressand vector and txk
design matrix. The complex structure incorporated into the disturbance
vector VT results from the successive solution of (2) in terms of BT"